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Illustrative Math
Grade 6
Lesson 10: Comparing Situations by Examining Ratios
Let’s use ratios to compare situations.
Illustrative Math Unit 6.2, Lesson 10 (printable worksheets)
Lesson 10 Summary
The following diagram shows how to use ratios to compare situations.
10.1 Treadmills
Mai and Jada each ran on a treadmill. The treadmill display shows the distance, in miles, each person ran and the amount of time it took them, in minutes and seconds.

What is the same about their workouts? What is different about their workouts?

If each person ran at a constant speed the entire time, who was running faster? Explain your reasoning.
Scroll down the page for the answers to Lin’s and Noah’s Sparkling Orange Juice Problems.
10.2  Concert Tickets
Diego paid $47 for 3 tickets to a concert. Andre paid $141 for 9 tickets to a concert. Did they pay at the same rate? Explain your reasoning.
Open applet for double number line
10.3  Sparkling Orange Juice
Lin makes sparkling orange juice by mixing 3 liters of orange juice with 4 liters of soda water. Noah makes sparkling orange juice by mixing 4 liters of orange juice with 5 liters of soda water. How do the two mixtures compare in taste? Explain your reasoning. If you get stuck, you can draw double number line diagrams to represent each situation.
Open applet for double number line
Are you ready for more?
 How can Lin make her sparkling orange juice taste the same as Noah’s just by adding more of one ingredient? How much will she need?
 How can Noah make his sparkling orange juice taste the same as Lin’s just by adding more of one ingredient? How much will he need?
Glossary Terms
same rate
We use the words same rate to describe two situations that have equivalent ratios.
For example, a sink is filling with water at a rate of 2 gallons per minute. If a tub is also filling with water at a rate of 2 gallons per minute, then the sink and the tub are filling at the same rate.
Lesson 10 Practice Problems
 A slug travels 3 centimeters in 3 seconds. A snail travels 6 centimeters in 6 seconds. Both travel at constant speeds. Mai says, “The snail was traveling faster because it went a greater distance.” Do you agree with Mai? Explain or show your reasoning.
 If you blend 2 scoops of chocolate ice cream with 1 cup of milk, you get a milkshake with a stronger chocolate flavor than if you blended 3 scoops of chocolate ice cream with 2 cups of milk. Explain or show why.
 There are 2 mixtures of light purple paint.
 Mixture A is made with 5 cups of purple paint and 2 cups of white paint.
 Mixture B is made with 15 cups of purple paint and 8 cups of white paint.
Which mixture is a lighter shade of purple? Explain your reasoning.
 Tulip bulbs are on sale at store A, at 5 for $11.00, and the regular price at store B is 6 for $13. Is each store pricing tulip bulbs at the same rate? Explain how you know.
 A plane travels at a constant speed. It takes 6 hours to travel 3,360 miles.
a. What is the plane’s speed in miles per hour?
b. At this rate, how many miles can it travel in 10 hours?
 A pound of ground beef costs $5. At this rate, what is the cost of:
a. 3 pounds?
b. 1/2 pound?
c. 1/4 pound?
d. 3/4 pound?
e. 3 3/4 pounds?
 In a triple batch of a spice mix, there are 6 teaspoons of garlic powder and 15 teaspoons of salt. Answer the following questions about the mix. If you get stuck, create a double number line.
a. How much garlic powder is used with 5 teaspoons of salt?
b. How much salt is used with 8 teaspoons of garlic powder?
c. If there are 14 teaspoons of spice mix, how much salt is in it?
d. How much more salt is there than garlic powder if 6 teaspoons of garlic powder are used?
The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.
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